## Abstract

We present an estimate for the convergence rate of the Dirichlet-Neumann

iteration for the discretized unsteady transmission problem. Specifically, we consider the coupling of two heat equations on two identical squared domains. The Laplacian is discretized by second order central finite differences and the implicit Euler method is used for the time discretization. For the semidiscrete case, Henshaw and Chad provided in

2009 a method to analyse stability and convergence speed based on applying the continuous Fourier transform to the semi-discretized equations. Numerical results for the fully discrete case show differences, which is why we propose a complementary analysis based on approximating the spectral radius of the iteration matrix. Numerical results are presented to illustrate the analysis.

iteration for the discretized unsteady transmission problem. Specifically, we consider the coupling of two heat equations on two identical squared domains. The Laplacian is discretized by second order central finite differences and the implicit Euler method is used for the time discretization. For the semidiscrete case, Henshaw and Chad provided in

2009 a method to analyse stability and convergence speed based on applying the continuous Fourier transform to the semi-discretized equations. Numerical results for the fully discrete case show differences, which is why we propose a complementary analysis based on approximating the spectral radius of the iteration matrix. Numerical results are presented to illustrate the analysis.

Original language | English |
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Title of host publication | VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015), Proceedings of the |

Editors | Bernhard A. Schrefler, Eugenio Oñate, Manolis Papadrakakis |

Publisher | CIMNE |

Pages | 452-463 |

Number of pages | 12 |

ISBN (Print) | 978-84-943928-3-2 |

Publication status | Published - 2015 |

Event | VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015) - Venice (Italy) Duration: 2015 May 18 → 2015 May 20 |

### Conference

Conference | VI International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015) |
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Period | 2015/05/18 → 2015/05/20 |

### Bibliographical note

The complete proceedings of the conference may be found at:http://congress.cimne.com/coupled2015/frontal/doc/Ebook_COUPLED_15.pdf

## Subject classification (UKÄ)

- Computational Mathematics

## Free keywords

- Dirichlet-Neumann Iteration
- Fixed Point Iteration
- Transmission Problem
- Coupled Problems
- Thermal Fluid Structure Interaction